Yes, you should set up the tank now. :happy:
Cleaning the slime usually doesn't hurt anything. Cleaning the ornaments and rocks is usually OK too, except that your tank has a rather small filter, so a larger proportion of the beneficial bacteria were on the rocks and decorations. So if your cycle weren't already probably crashed, you might have seen ammonia and nitrite spikes.
Did you clean the sponge filter? (You should squeeze them out in a small container of tank water once a week. Don't use tap water unless it is dechlorinated.)
Here is what I recommend for a fishless (axolotl-less) cycle.
1) Get a bigger filter (a sponge filter is good for axolotl tank, but make sure it is sized to handle a larger tank than the one you have) and set it up in the tank.
2) Get a test kit that tests for ammonia, nitrite, nitrate, and pH. Check your tank to see what the current levels are. (Read the directions - some tests have to sit before you check the reading.)
3) Get some pure ammonia (no additives like scent).
4) Add a food pellet to the tank and leave it there. (It provides trace elements for the bacteria.)
5) Add small quantities of ammonia (spoonful at a time) to the tank until the ammonia rises to about 4 ppm.
6) Check the pH, ammonia, and nitrites the next day. If the ammonia has dropped noticeably, hurray! If the pH has dropped below 6.5, change 25% of the water. (Low pH will also have negative impact on the cycle.)
7) Repeat the previous two steps until the ammonia and nitrite drop to 0 by the next day.
8) Do a 90-100% water change (dechlorinate the water!).
9) Reintroduce Hikaru to the tank. (Float her container in the tank until the temperature is the same, etc.) If she is coming straight out of the fridge, put her container in a cooler and let it warm up slowly to about the same temperature as the tank first.
You can cycle with Hikaru in the tank, but that will take longer and take more work, since you will need to keep the ammonia and nitrite low by doing frequent water changes water changes. The advantage is, then you don't need to buy ammonia since Hikaru would supply her own. :happy:
If Hikaru seems recovered before the fishless cycle is complete, you can keep her in a smaller container outside of the tank and do 100% water changes every day.
I consider cycling a tank to be very educational, and you son is the right age to be educated.

Just make sure he reads and understands everything, and double check all of the conditions before you let him put Hikaru back in the tank!